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In this paper the relationship between locally reachable sets for a fixed set of controls in the Lie algebra of a Lie group and the local semigroups generated by the corresponding one-parameter semigroup is considered. It is convenient to carry out the investigation in the Lie algebra itself, and the appropriate machinery for doing this is first developed. It is shown that local semigroups contain locally reachable sets. A general criterion (rerouting) is developed for the converse inclusion, and it is shown that if the set of controls is contained in a proper cone or is a Lie wedge (i.e., the tangent of a local semigroup), then it is the case that locally reachable sets contain local semigroups. © 1990 Rocky Mountain Mathematics Consortium.

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Rocky Mountain Journal of Mathematics

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